The series combination of two batteries, both of the same emf $10 \mathrm{\;V},$ but different internal resistance of $20\; \Omega$ and $5\; \Omega,$ is connected to the parallel combination of two resistors $30\; \Omega$ and $\mathrm{R}\; \Omega .$ The voltage difference across the battery of internal resistance $20\; \Omega$ is zero, the value of $\mathrm{R}(\text { in } \Omega)$ is
JEE MAIN 2020, Diffcult
Download our app for free and get started
$\mathrm{E}_{1} =\mathrm{E}-\mathrm{ir}$ $=10-\mathrm{i} \times20=0$
$\mathrm{i}=0.5 \mathrm{A}$
$\mathrm{E}_{2}=\mathrm{E}-\mathrm{ir}$
$=10-0.5 \times 5$ $=7.5 \mathrm{V}$
$\mathrm{E}_{\mathrm{net}}=\mathrm{E}_{1}+\mathrm{E}_{2}=7.5 \mathrm{V}$
$\mathrm{i}=\mathrm{i}_{1}+\mathrm{i}_{2}$
$0.5=\frac{7.5}{x}+\frac{7.5}{30}$
$\mathrm{x}=30 \Omega$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A metallic block has no potential difference applied across it, then the mean velocity of free electrons is $T$ = absolute temperature of the block)View Solution
- 2Five cells each of emf $E$ and internal resistance $r$ are connected in series. Due to oversight one cell is connected wrongly. The equivalent internal resistance of the combination is ........... $r$View Solution
- 3View SolutionThe magnitude and direction of the current in the circuit shown will be
- 4A cell of e.m.f. $E$ is connected with an external resistance $R$, then p.d. across cell is $V$. The internal resistance of cell will beView Solution
- 5View SolutionFor measurement of potential difference, potentiometer is preferred in comparison to voltmeter because
- 6If $n, e, \tau$ and $m$ are representing electron density, charge, relaxation time and mass of an electron respectively, then the resistance of a wire of length / and cross-sectional area $A$ is given byView Solution
- 7In $a$ wire of cross-section radius $r$, free electrons travel with drift velocity $v$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2v$?View Solution
- 8Suppose the drift velocity $v_d$ in a material varied with the applied electric field $E$ as ${v_d}\, \propto \,\sqrt E $ .Then $V - I$ graph for a wire made of such a material is best given byView Solution
- 9The resistance of a wire is $5 \Omega$. It's new resistance in ohm if stretched to $5$ times of it's original length will be :View Solution
- 10If two bulbs of wattage $25$ and $30$, each rated at $220\, volts$, are connected in series with a $440$ $volt$ supply, which bulb will fuseView Solution